vertex (3, 1)
directrix y = 6
The equation of a parabola is
[tex]y=\frac{1}{4(f-k)}(x-h)^2+k[/tex]
where,
(h,k) is the vertex and (h,f) is the focus
Thus,
h = 3
k = 1
The distance from the focus to the vertex is equal to the distance from the vertex to the directrix, then f - k = k - 6
replace k=1 and solve for f,
[tex]\begin{gathered} f-1=1-6 \\ f=-5+1 \\ f=-4 \end{gathered}[/tex]
Thus,
h = 3
k = 1
f = -4
therefore, the equation of the parabola is,
[tex]\begin{gathered} y=\frac{1}{4*(-4-1)}(x-3)^2+1 \\ \\ y=-\frac{1}{20}(x-3)^{2}+1 \end{gathered}[/tex]
